Please define clearly what you mean by "through no fault of their own" then.

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One cannot observe any past behavior(s) such as smoking, eating excessively, consumption of excess sugar, breathing coal dust, working with asbestos, etc. that would have a direct causative effect on the disease/sickness that they currently suffer.

Well of course but if you run a hospital or are a decision maker in medicare you have X amount of funds to spread around.

Hypothetically, the cost of a heart transplant to give an aged person a few more years of life could be used to enhance the health of a greater number of younger people in a more long term manner.

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Te futueo et caballum tuum

1986 300SDL, 362K
1984 300D, 138K

Younger people get hearts before the older people,; actually that holds true for all organs. Now, however there is a campaign that EVERYONE can be a donor even patients with terminal illnesses , even AIDS patients! The reasoning behind it is that an old o=donor could be used for an older recipient who otherwise would not have received an organ because of a younger recipient waiting in line who automatically get bumped up ahead of him by virtue of him being younger. An HIV patient can donate an organ to another HIV positive patient and so on. Since these days, an HIV positive person has an almost equal lifespan as one who is negative and almost has about the same quality of life, then why not?

Well, the good news is that he no longer has to hold the cigarette to his lips.